Indian Mathematics & Astronomy

This folio from a Sanskrit manuscript, likely a treatise on Jyotisha (traditional Indian astronomy and astrology), features a precisely drawn red grid used for astronomical calculations or mapping planetary positions. The lower portion of the page is filled with dense, calligraphic Devanagari text that provides instructions or commentary on the mathematical data above. Executed with black ink and red pigment on paper, it represents the scientific and scholarly traditions of Northern India, particularly the region of Jammu and Kashmir.

This page is from the Siddhāntatattvaviveka, a seminal 17th-century Sanskrit treatise on mathematical astronomy by the scholar Kamalākara. The illustration features a sophisticated geometric diagram used to derive trigonometric values, labeled with terms like 'jya' (sine) and 'koti' (cosine). The work is historically significant for its synthesis of traditional Indian astronomical methods with concepts from contemporary Islamic mathematical traditions.

A page from a printed edition of Bhaskara II's 12th-century mathematical masterpiece, the Lilavati. The illustration presents geometric diagrams and Sanskrit text detailing the calculations for side lengths of regular polygons—ranging from a pentagon to an octagon—inscribed within a circle of a specified diameter.

This page is from a treatise on 'Kṣetravyavahāra' (mensuration), a branch of classical Indian mathematics. It features several geometric diagrams depicting quadrilaterals and a triangle, with dimensions and calculations provided in Devanagari numerals. The accompanying text, written in both Sanskrit and Hindi, explains the trigonometric and geometric formulas used to determine properties such as the internal perpendiculars and areas of these figures.

A page from a scholarly edition of the 'Gaṇitasārasaṅgraha', a 9th-century mathematical treatise by the Indian Jain scholar Mahāvīrācārya. The text details algebraic rules for determining the properties of circles and features geometric diagrams of traditional symbolic shapes—including the 'vajra' (thunderbolt) and 'yava' (grain)—used for area calculations.

This manuscript leaf originates from a Sanskrit astronomical treatise, likely a Jyotisha text used for calculating celestial movements. It features a central grid containing numerical data, with headers that abbreviate the names of the Sun, Moon, and planets (such as 'Jiva' for Jupiter and 'Shukra' for Venus) to facilitate complex astrological computations. The text is meticulously handwritten in Devanagari script, with red-ink ruling used to organize the tabular information.

A page from a 1912 scholarly edition of the 9th-century Sanskrit mathematical treatise 'Gaṇitasārasaṅgraha' by Mahāvīra. It features numbered diagrams illustrating various curvilinear areas such as conchiform, concave, and convex shapes, alongside different forms of the annulus. The text serves to translate and preserve medieval Indian geometric concepts for a modern academic audience.

This technical diagram from a Sanskrit astronomical treatise illustrates the derivation of trigonometric functions within a circle. It features traditional Indian mathematical labels like 'jya' (sine) and 'kotijya' (cosine), used for calculating planetary positions as part of the 'Spashtadhikara' (True Places of Planets) chapter.